Finding Discontinuous Solutions to the Differential-Difference Equations by the Homotopy Analysis Method
ZOU Li1,2,5**, ZOU Dong-Yang1,2, WANG Zhen4, ZONG Zhi2,3
1School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116085 2State Key Laboratory of Structure Analysis for Industrial Equipment, Dalian 116085 3School of Naval Architecture and Ocean Engineering, Dalian University of Technology, Dalian 116085 4Department of Applied Mathematics, Dalian University of Technology, Dalian 116085 5Department of Mathematics, Fluid Dynamics Group, Imperial College, London SW7 2AZ, UK
Abstract：An analytic method, namely the homotopy analysis method, is applied to nonlinear problems with discontinuity governed by the differential-difference equation. Purely analytic solutions are given for nonlinear problems with discontinuity with a global convergence. This method provides a new analytical approach to solve nonlinear problems with discontinuity. Comparisons are made between the results of the proposed method and the exact solutions. The results reveal that the proposed method is very effective and convenient.
(Ordinary and partial differential equations; boundary value problems)
引用本文:
. [J]. Chin. Phys. Lett., 2013, 30(2): 20204-020204.
ZOU Li, ZOU Dong-Yang, WANG Zhen, ZONG Zhi. Finding Discontinuous Solutions to the Differential-Difference Equations by the Homotopy Analysis Method. Chin. Phys. Lett., 2013, 30(2): 20204-020204.
2013, Vol. 30 
